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Relativistic Interacting Integrable Elliptic Tops

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Abstract

We propose a relativistic generalization of integrable systems describing M interacting elliptic gl(N) Euler-Arnold tops. The obtained models are elliptic integrable systems that reproduce the spin elliptic GL(M) Ruijsenaars-Schneider model with N = 1 and relativistic integrable GL(N) elliptic tops with M = 1. We construct the Lax pairs with a spectral parameter on the elliptic curve.

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Authors and Affiliations

  1. Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

    A. V. Zotov

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Correspondence to A. V. Zotov.

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Conflicts of interest. The author declares no conflicts of interest.

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This research is supported by a grant from the Russian Science Foundation (Project No. 19-11-00062).

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 201, No. 2, pp. 175–192, November, 2019.

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Zotov, A.V. Relativistic Interacting Integrable Elliptic Tops. Theor Math Phys 201, 1565–1580 (2019). https://doi.org/10.1134/S0040577919110035

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